In this chapter we focus on the concept of proof, which is important for students'
mathematical education but also hard for teachers to teach and difficult for students to learn …

In the chapter on proof in the previous PME Research Handbook, Mariotti (2006) observed
that there had seemed to be “a general consensus on the fact that the development of a …

Although proving is core to mathematics as a sense-making activity, it currently has a
marginal place in elementary classrooms internationally. Blending research with practical …

The concept of proof has attracted considerable research attention over the pastdecades in
part due to its indisputable importance to the discipline of mathematics and tostudents' …

This paper reports a mixed-methods, causal-comparative study of two instructional
approaches in a differential equations course for engineering undergraduates. One …

Students' apprenticeship into proof-oriented mathematical practice requires that they
become aware of a range of conventions and assumptions about mathematical language …

We discuss whether a generic argument can be considered a proof. Two positions on this
question have recently been published which focus on the fussiness of an argument as a …

The use of examples has been identified as a pedagogical tool for proof presentations,
however, the types and uses of examples in the context of proof presentations in advanced …

In this paper, we explore the role that examples play as mathematicians formulate
conjectures, and we describe and exemplify one particular example-related activity that we …

We examined the proof-writing behaviors of six highly successful mathematics majors on
novel proving tasks in calculus. We found two approaches that these students used to write …